On Greenberg--Benois $\mathcal{L}$-invariants and Fontaine--Mazur $\mathcal{L}$-invariants

Abstract

We prove a comparison theorem between Greenberg--Benois $\mathcal{L}$-invariants and Fontaine--Mazur $\mathcal{L}$-invariants. Such a comparison theorem supplies an affirmative answer to a speculation of Besser--de Shalit.